Orbital population

The Lowdin population analysis scheme was created to circumvent some of the unreasonable orbital populations predicted by the Mulliken scheme, which it does. It is different in that the atomic orbitals are first transformed into an orthogonal set, and the molecular orbital coefficients are transformed to give the representation of the wave function in this new basis. This is less often used since it requires more computational work to complete the orthogonalization and has been incorporated into fewer software packages. The results are still basis-set-dependent. 

HOMO and LUMO energies FMO reactivity indices Refractivity Total energy Ionization potential Electron affinity Energy of protonation Orbital populations Frontier orbital densities Superdelocalizabilities... 

Table 6. Net orbital populations of ClFe(Et2dtc)2 and Fe(Et2 fc)3 and the resulting QS.

Atomic orbital populations and resulting QS in a crystal field model. 

Fig. 5.5 Lack of correlation between the As orbital population and the valence contribution to the isomer shift (taken from [19])...

In the disilane molecule, for example, the silicon atoms exhibit significant electron deficiency. The atomic orbital population and its equivalent in ethane is recorded in Table 3. 

Table 3. Atomic orbital population of silicon and carbon in disilane and ethane, respectively.

Several facts are apparent when the data shown in Table 1.1 are considered. In order to see some of the specific results more clearly, Figure 1.10 has been prepared to show how the electron affinity varies with position in the periodic table (and therefore orbital population). From studying Figure 1.10 and the data shown in Table 1.1, the following relationships emerge ... 

Arrange the species 022-, 02+, 02, and 02- in the order of decreasing bond length. Explain this order in terms of molecular orbital populations. 

Electrons generally fill orbitals in atoms as the sum (n + /) increases. Therefore, after the 6 s orbital (for which n + l = 6) is filled at Ba, it would be expected that the next orbitals populated would be those for which the sum (n I 2) 7 but having the lowest n giving that sum. The corresponding orbitals would be... 

TABLE 10. MP2/TZDP Mulliken atomic orbital populations for X in XH3Ya ... 

Natural population analysis of transition-metal-fluoride wavefunctions gives orbital populations that are generally consistent with the expected configurations, but with large departures from an idealized ionic picture. Table 2.4 compares the... 

From (5.20) and (5.22) and the expression qf = 2Qih/e2Q, which relates the principal values qf of the EFG tensor to the experimentally determined components Qt of the tensor Q, one obtains the following formulae for the angle 6 and the orbital populations ... 

Nitrogen 2p-orbital populations have been calculated from the experimental quadrupole tensors using the TD theory. The lone pair populations (Ag) = 1.838 and [Pg.67]

Spijkerman, Ruegg, and May (41) have given a modified WWJ plot which uses the WWJ calibration points but uses Gray s 4s occupation numbers (2, 35) for some ferrous compounds to determine the slope of the line for this valence state. Apparently they did not take into account the 3d orbital population given by Gray s calculations and seem to have been unable to apply similar calculations to ferric compounds. 

Vith group is an indication of a decrease in the IT carbonyl orbital population, as expected from the decrease of the P(3d) orbital... 

For instance, the (pentaphenylcyclopentadienyl) cobalt dicarbonyl anion-radical complex [(q-C5Ph5)Co(CO)2] has (n + 1) metal orbital populated with an unpaired electron, according to calculations by Connelly et al. (1986). In contrast, reduction of (bpy)Cr(CO)4 (bpy = 2,2 -bipyridyl) to its anion radical is known to occur without any major change in its structure or composition. 

Charges on atoms Valence orbital population Spin distribution ... 

---